The strain rosette is a fundamental of analytical strain analysis, as explained in the engineering text “Theory of Elasticity” by Timoshenko and Goodier: The strains, or unit elongations, on a surface are usually most conveniently measured by means of electric-resistance strain gages. The use of these gages is simple when the principal directions are known. One gage is placed along each principal direction and an analog of strain is measured and calibrated to indicate strains ε1, ε2. The principal stresses σ1, σ2 can then be calculated from Hooke's law, with σx=σ1, and σy=σ2, and with σz=0 on the assumption that there is no stress acting on the surface to which the gauges are attached. Then:(1−ν2)σ1=E(ε1+νε2) and (1−ν2)σ2=E(ε2+νε1)
When the principal directions are not known in advance, three measurements are needed. Thus, the state of strain is completely determined if εx, εy, and νxy can be measured. But since strain gages, and particularly electrical resistance strain gages, measure extensions, and not shearing strain directly, it is convenient to measure the unit elongations in three directions at the point. Such a set of electrical resistance gages is commonly called a “strain rosette” because the gages are arranged in the pattern of a strain rosette; however, “strain rosette” is used here in its original sense (as set forth in the definitions below), rather than to denote a configuration of electrical resistance gages.
A Mohr strain circle can be constructed for a strain rosette, and the differential equations of equilibrium for a small rectangular block of edges h, k, and unity can be derived. If X, Y denote the components of body force per unit volume, the equation of equilibrium for forces in the x-direction is(σx)1k−(σx)3k+(τxy)2h−(τxy)4h+Xhk=0,where σx, σy, and τxy refer to the point x, y, the mid-point of the small rectangular block, and where (σx)1, (σx)3, etc. denote the values at the mid-points of the faces of the rectangle. The dividing by hk,                                           (                          σ              x                        )                    1                -                              (                          σ              x                        )                    3                    h        +                                                      (                              τ                xy                            )                        2                    ⁢          h                -                                            (                              τ                xy                            )                        4                    ⁢          h                    k        +    X    =  0
If the block is taken smaller and smaller, that is, h→0, h→0, the limit of [(σx)1, −(σx)3]/k is ∂σx/∂x by the definition of such a derivative. Similarly, [(τxy)2, −(τxy)4]/k is ∂τxy/∂y. The equation of equilibrium for forces in the y-direction is obtained in the same manner.
Strain measurements made with electrical resistance gages in a rosette pattern are subject to the same errors (thermal output, transverse sensitivity, leadwire resistance effects, etc.) as those made with single-element strain gages.
Letters Patent of U.S. Pat. No. 4,591,996 to Vachon and Ranson discloses optical strain measurement using correlation of speckle patterns reflected from an illuminated optically diffuse surface. The speckle patterns are random signals that are characteristics of the surface area under investigation. Each area of the surface has a unique pattern just as each individual has unique facial characteristics. Correlating the movement of the speckle pattern of a surface undergoing deformation using machine vision to record the speckle pattern movement as a function of time permits the determination of strain.
Technical efforts have continued in the area of optical correlation of surface images to detect strain. Specifically, these efforts include, among other things: (1) optical detection of edges of images on surfaces as well as optical detection of edges of surfaces, (2) optical correlation of dot and other geometric patterns applied to surfaces, and (3) optical correlation of the movement of centroids of geometric patterns applied to surfaces. All of these analytical and experimental efforts have been directed to optical detection of strain.
Single-element strain gages, electrical resistance gages arranged in a rosette pattern employ analog techniques, rather than measuring strain directly. Previous optical correlation techniques calculate strains using a convolution integral, and also do not measure strain directly.
It is to the provision of a strain gage that can measure strain directly, as well as assessing fatigue damage, that the present invention is directed.